Column multiplication

In your book, Maths Mela (Chapter 6, The Dairy Farm), a dairy cooperative gets its milk from 268 villagers, and each villager has at least 4 cows. So there are at least 268 × 4 cows. Mili's father has taught her to multiply in columns, using the place values of the digits.

Start with the ones: 4 × 8 = 32. Write 2 in the ones column and carry the 3 tens to the tens column. Next the tens: 4 × 6 tens = 24 tens, and the carried 3 tens make 27 tens. Write 7 in the tens column and carry the 2 hundreds. Last the hundreds: 4 × 2 hundreds = 8 hundreds, and the carried 2 hundreds make 10 hundreds. Write 10. So 268 × 4 = 1,072. The carry is added AFTER multiplying: the 3 tens are added to 4 × 60, not to 60.

Among the villagers there are 453 Gir cows, a cow breed from Gujarat, and each gives 13 litres of milk a day. For 453 × 13, first multiply by the 3 ones: 3 × 453 = 1,359. Then multiply by the 1 ten: 1 ten × 453 = 453 tens = 4,530. That is why we write a 0 in the ones place of the second row. Add the rows: 1,359 + 4,530 = 5,889 litres.

The cooperative sells ghee at ₹574 a kg and makes about 125 kg a month. 574 × 125 has three rows: 5 × 574 = 2,870, then 20 × 574 = 11,480 (one zero, for tens), then 100 × 574 = 57,400 (two zeros, for hundreds). Add them: 2,870 + 11,480 + 57,400 = 71,750. The cooperative earns ₹71,750.